Modern driver assistance systems are known which, for example, include a vehicle speed controller or an adaptive vehicle speed controller having brake intervention. These vehicle speed controllers can drive a drive unit as well as a brake system of a vehicle via suitable interfaces. Here, it must be avoided as best as possible that brake system and drive unit operate in opposition to each other. For this reason, a brake intervention via the vehicle speed controller is not enabled when there is a drive of the drive unit with a drive torque which is greater than the minimum possible drive torque referred to the instantaneous gear. In active brake control via the vehicle speed controller, the minimum possible drive torque referred to the instantaneous gear is requested by the drive unit. Because of such a drive, the drive unit is driven during braking at the minimum possible torque. The drive unit can cause the transmission to adjust the maximum possible gear which is permitted at the instantaneous speed of the vehicle. With this gear selection, the case can occur that the engine rpm assumes such low values that no overrun switchoff of the engine is possible and fuel must be consumed notwithstanding the braking. Even if the engine rpm permits an economical overrun switchoff, no optimal support or relief of the brake system is obtained via the described gear selection.